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It looks like you've uploaded an image of a math problem involving finding the approximate coordinates of all points where the function's derivative is zero (critical points). Let me take a closer look and provide a detailed solution.From the image, the task is to find the approximate coordinates of all points where the derivative of the function is zero (i.e., where the graph has horizontal tangents or critical points).

To identify these points, we need to look for locations on the graph where the slope of the function is zero, which corresponds to the peaks, troughs, or flat points.

Based on the graph:

1. **Approximate Critical Points:**
   - There appears to be a critical point near \((-2, 2)\).
   - Another critical point is around \((0, -2)\).
   - A third critical point is approximately \((2, 0)\).

These points are estimated based on the visible intersections where the graph levels out horizontally. If any of these do not exist or if these are not clear, you might need to click the graph for a closer view to fine-tune these coordinates.

Would you like a more detailed explanation, or do you have any other questions? Here are some further questions that could help expand your understanding:

1. How can you determine if these critical points are maxima, minima, or saddle points?
2. What role does the second derivative play in analyzing these points?
3. How can you use these critical points to sketch a rough graph of the function's derivative?
4. What happens to the function's behavior around these critical points?
5. How do these critical points relate to the increasing or decreasing nature of the function?

**Tip:** Always double-check the coordinates by zooming in on the graph to get a precise reading, especially when working with critical points.

Find the approximate coordinates of all points where the function's derivative is zero (i.e., where the graph has horizontal tangents or critical points).

Learn how to find the approximate coordinates of critical points where the derivative of a function is zero. This problem covers key calculus concepts such as critical points, graph analysis, and the first derivative test. Suitable for high school calculus students.

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